PURPOSE: Glaucoma is a leading cause of irreversible blindness, and accurate cup-to-disc ratio (CDR) measurement is essential for early detection. This study presents an enhanced deep learning–based system for automated CDR estimation and glaucoma screening. METHODS: We propose an end-to-end framework consisting of three modules: (1) optic cup and disc segmentation using an enhanced dual encoder–decoder network (E-DCoAtUNet), (2) a conditional random field (CRF) post-processing module for boundary refinement, and (3) a measurement module for vertical CDR calculation and glaucoma classification. The model was trained and evaluated on the Drishti-GS dataset and validated on the REFUGE dataset to assess generalizability. RESULTS: The system achieved Dice scores of 97.6% for the optic disc and 90.8% for the optic cup, further improved by CRF refinement. Automated CDR estimation showed strong agreement with expert annotations (Pearson’s r = 0.9190, MAE = 0.0387). For glaucoma screening, the system demonstrated reliable performance across both datasets, highlighting its robustness and clinical applicability. CONCLUSION: The proposed E-DCoAtUNet-based system provides a fully automated, interpretable, and precise solution for glaucoma screening. By integrating advanced segmentation, boundary refinement, and accurate measurement, it ensures consistent CDR evaluation even under challenging imaging conditions, and demonstrates strong potential for real-world clinical application.

Abstract Dragonfly networks have significant advantages in data exchange due to the small network diameter, low cost and modularization. A graph $G$ is $vertex$-$pancyclic$ if for any vertex $u\in V(G)$, there exist cycles through $u$ of every length $\ell $ with $3\leq \ell \leq |V(G)|$. A graph $G$ is $Hamiltonian$-$connected$ if there exists a Hamiltonian path between any two distinct vertices $u,v\in V(G)$. In this paper, we mainly research the pancyclic and Hamiltonian properties of the dragonfly network $D(n,h)$, and find that it is Hamiltonian with $n\geq 1,\,\,h\geq 2$, pancyclic, vertex-pancyclic and Hamiltonian-connected with $n\geq 4,\,\,h\geq 2$.

Abstract. A graph [Formula: see text] is called [Formula: see text]-free if it does not contain any cycle of length [Formula: see text]. In 1962, Erdös (together with Gallai), and independently Andrásfai, proved that every [Formula: see text]-vertex triangle-free graph with more than [Formula: see text] edges is bipartite. In this paper, we extend their result and show that for [Formula: see text] and [Formula: see text], every [Formula: see text]-vertex [Formula: see text]-free graph with more than [Formula: see text] edges can be made bipartite by either deleting at most [Formula: see text] vertices or deleting at most [Formula: see text] edges. The construction shows that this is best possible.

Many of the tissues/lesions in the medical images may be ambiguous. Therefore, medical segmentation is typically annotated by a group of clinical experts to mitigate personal bias. A common solution to fuse different annotations is the majority vote, e.g., taking the average of multiple labels. However, such a strategy ignores the difference between the grader expertness. Inspired by the observation that medical image segmentation is usually used to assist the disease diagnosis in clinical practice, we propose the diagnosis-first principle, which is to take disease diagnosis as the criterion to calibrate the inter-observer segmentation uncertainty. Following this idea, a framework named Diagnosis-First segmentation Framework (DiFF) is proposed. Specifically, DiFF will first learn to fuse the multi-rater segmentation labels to a single ground-truth which could maximize the disease diagnosis performance. We dubbed the fused ground-truth as Diagnosis-First Ground-truth (DF-GT). Then, the Take and Give Model (T&G Model) to segment DF-GT from the raw image is proposed. With the T&G Model, DiFF can learn the segmentation with the calibrated uncertainty that facilitate the disease diagnosis. We verify the effectiveness of DiFF on three different medical segmentation tasks: optic-disc/optic-cup (OD/OC) segmentation on fundus images, thyroid nodule segmentation on ultrasound images, and skin lesion segmentation on dermoscopic images. Experimental results show that the proposed DiFF can effectively calibrate the segmentation uncertainty, and thus significantly facilitate the corresponding disease diagnosis, which outperforms previous state-of-the-art multi-rater learning methods.

Abstract The problem of finding the maximum independent sets (or maximum cliques) of a given graph is fundamental in graph theory and is also one of the most important in terms of the application of graph theory. Let $A(n,d,w)$ be the size of the maximum independent set of $Q_{n}^{(d-1,w)}$, which is the induced subgraph of points of weight $w$ of the $d-1^{th}$-power of $n$-dimensional hypercubes. In order to further understand and study the dependent set of $Q_{n}^{(d-1,w)}$, we explore its clique number and the structure of the maximum clique. This paper obtains the clique number and the structure of the maximum clique of $Q_{n}^{(d-1,w)}$ for $5\leq d\leq 6$. Moreover, the characterizations for $A(n,d,w)=2$ and $3$ are also given.

Abstract Zhu et al. introduced the $h$-edge tolerable diagnosability to measure the fault diagnosis capability of a multiprocessor system with faulty links. This kind of diagnosability is a generalization of the concept of traditional diagnosability. A graph is called a maximally connected graph if its minimum degree equals its vertex connectivity. It is well-known that many irregular networks are maximally connected graphs and the $h$-edge tolerable diagnosabilities of these networks are unknown, which is our motivation for research. In this paper, we obtain the lower bound of the $h$-edge tolerable diagnosability of a class of $t$-connected graphs and establish the $h$-edge tolerable diagnosability of a class of maximally connected graphs under the PMC model and the MM$^*$ model, which extend some results in (Hakimi, S.L. and Amin, A.T. (1974) Characterization of connection assignment of diagnosable systems. IEEE Trans. Comput., 23, 86–88), (Chang, C.P., Lai, P.L., Tan, J.J.M. and Hsu, L.H. (2004) Diagnosability of t-connected networks and product networks under the comparison diagnosis model. IEEE Trans. Comput., 53, 1582–1590) and (Lian, G., Zhou, S., Hsieh, S.Y., Liu, J., Chen, G. and Wang, Y. (2019) Performance evaluation on hybrid fault diagnosability of regular networks. Theoret. Comput. Sci., 796, 147–153).

Retinal vein occlusion (RVO) is the second common cause of blindness following diabetic retinopathy. The manual screening of fundus images to detect RVO is time consuming. Deep‐learning techniques have been used for screening RVO due to their outstanding performance in many applications. However, unlike other images, medical images have smaller lesions, which require a more elaborate approach. To provide patients with an accurate diagnosis, followed by timely and effective treatment, we developed an intelligent method for automatic RVO screening on fundus images. Swin Transformer learns the hierarchy of low‐to high‐level features like the convolutional neural network. However, Swin Transformer extracts features from fundus images through attention modules, which pay more attention to the interrelationship between the features and each other. The model is more universal, does not rely entirely on the data itself, and focuses not only on local information but has a diffusion mechanism from local to global. To suppress overfitting, we adopt a regularization strategy, label smoothing, which uses one‐hot to add noise to reduce the weight of the categories of true sample labels when calculating the loss function. The choice of different models using a 5‐fold cross‐validation on our own datasets indicates that Swin Transformer performs better. The accuracy of classifying all datasets is 98.75 ± 0.000, and the accuracy of identifying MRVO, CRVO, BRVO, and normal, using the method proposed in the paper, is 94.49 ± 0.094, 99.98 ± 0.015, 98.88 ± 0.08, and 99.42 ± 0.012, respectively. The method will be useful to diagnose RVO and help decide grade through fundus images, which has the potency to provide patients with further diagnosis and treatment.

Rotating source beamforming techniques have been effective means of noise localization on rotary machines. In this letter, we derive an alternative expression for modal composition beamforming (MCB) and subsequently consider the equivalent source assumption and cyclostationarity of the constant angular-speed rotating sound source so that a rotating sound source power (RSP) propagation model is derived. By estimating a suitable solution for the RSP model using the subspace variational Bayesian (SVB) technique with sparsity and total variation (TV) priors, the validity of the RSP model was established. According to the simulation results, the proposed RSP-SVB method leads to a significantly higher resolution than the MCB method. It can localize multiple fast-rotating sound sources accurately, rapidly, and effectively in environments with strong background noise interference. Therefore, our proposed RSP-SVB can offer a reliable solution for identifying fast-rotating blade noise.

The non-synchronous measurement (NSM) technology has been significantly developed. NSM at the coprime position (CP-NSM) is a measurement principle in two-dimensional (2D) acoustic imaging, wherein a planar array is moved to a coprime position for measurements. However, there are certain drawbacks to the measurement principles of spherical arrays in three-dimensional (3D) acoustic imaging. A measurement principle of 3D acoustic imaging has been investigated using 3D Non-Synchronous Measurements with a Central Reference based on Revolution and Autorotation (CR-NSM). The primary contributions of this CR-NSM are as follows: (1) A measurement principle for 3D non-synchronous measurements with a central reference based on revolution and autorotation is proposed. (2) The spatial resolution is primarily determined by the revolution in CR-NSM, and the side lobe is reduced by autorotation in CR-NSM. In the simulation results, the spatial resolution is obtained using CR-NSM for good imaging at low signal-to-noise ratios (SNR). Moreover, the cross-spectral matrix (CSM) completion error is enhanced by adding the phase relations between consecutive positions. The CR-NSM algorithm was developed according to the measurement principles of 3D acoustic imaging.

Abstract The diagnosability is one of the most important measures of the reliability of networks. Consider the setting where there are large-scale failures that disconnect the network and result in many components. Then, the diagnosability is closely related to the number of components. In this paper, we define and study the $\boldsymbol{g}$-component diagnosability of network $\boldsymbol{G}$, which is denoted by $\boldsymbol{ct_g(G)}$ and has not been addressed before. $\boldsymbol{ct_g(G)}$ is the maximum number of nodes in the faulty node set $\boldsymbol{F}$ of $\boldsymbol{G}$ such that $\boldsymbol{G-F}$ has at least $\boldsymbol{g}$ components and diagnosis model can identify all nodes in $\boldsymbol{F}$. Under PMC and MM$^*$ diagnosis models, we show that, in the hypercube $\boldsymbol{Q_n\ (n\geq 7)}$, $\boldsymbol{ct_{g+1}(Q_n)=-(1/2)g^2+(n-3/2)g+n}$ when $\boldsymbol{g\leq n-1}$. Moreover, we determine the $\boldsymbol{(n+1)}$-component diagnosability $\boldsymbol{ct_{n+1}(Q_n)=n^2/2+n/2-2}$ for $\boldsymbol{n\geq 7}$.

Periodicity is a frequently happening phenomenon for social interactions in temporal networks. Mining periodic communities are essential to understanding periodic group behaviors in temporal networks. Unfortunately, most previous studies for community mining in temporal networks ignore the periodic patterns of communities. In this paper, we study the problem of seeking periodic communities in a temporal network, where each edge is associated with a set of timestamps. We propose novel models, including$\sigma$-periodic$k$-core and$\sigma$-periodic$k$-clique, that represent periodic communities in temporal networks. Specifically, a$\sigma$-periodic$k$-core (or$\sigma$-periodic$k$-clique) is a$k$-core (or clique with size larger than$k$) that appears at least$\sigma$times periodically in the temporal graph. The problem of searching periodic core is efficient but the resulting communities may be not enough cohesive; the problem of enumerating all periodic cliques is not efficient (NP-hard) but the resulting communities are very cohesive. To compute all of them efficiently, we first develop two effective graph reduction techniques to significantly prune the temporal graph. Then, we transform the temporal graph into a static graph and prove that mining the periodic communities in the temporal graph equals mining communities in the transformed graph. Subsequently, we propose a decomposition algorithm to search maximal$\sigma$-periodic$k$-core, a Bron-Kerbosch style algorithm to enumerate all maximal$\sigma$-periodic$k$-cliques, and a branch-and-bound style algorithm to find the maximum$\sigma$-periodic clique. The results of extensive experiments on five real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.

We study a class of generic charging path optimization problems arising from emerging networking applications, where mobile chargers are dispatched to deliver energy to mobile agents (e.g., robots, drones, vehicles), which have specified tasks and mobility patterns. We instantiate our work by focusing on finding the charging path maximizing the number of nodes charged within a fixed time horizon. We show that this problem is APX-hard. By recursively decomposing the problem into sub-problems of searching sub-paths, we design quasi-polynomial-time algorithms achieving logarithmic approximation to the optimum charging path. Our approximation algorithms can be further adapted and extended to solve a variety of charging path optimization and scheduling problems with realistic constraints, such as limited time and energy budget.

Core decomposition is a fundamental operator in network analysis. In this paper, we study a problem of computing distance-generalized core decomposition on a network. A distance-generalized core, also termed (k, h)-core, is a maximal subgraph in which every vertex has at least k other vertices at distance no larger than h. The state-of-the-art algorithm for solving this problem is based on a peeling technique which iteratively removes the vertex (denoted by v) from the graph that has the smallest h-hop degree. The h-hop degree of a vertex v denotes the number of other vertices that are reachable from v within h hops. Such a peeling algorithm, however, needs to frequently recompute the h-hop degrees of v's neighbors after deleting v, which is typically very costly for a large h. To overcome this limitation, we propose an efficient peeling algorithm based on a novel h-hop degree updating technique. Instead of recomputing the h-hop degrees, our algorithm can dynamically maintain the h-hop degrees for all vertices via exploring a very small subgraph, after peeling a vertex. We show that such an h-hop degree updating procedure can be efficiently implemented by an elegant bitmap technique. In addition, we also propose a sampling-based algorithm and a parallelization technique to further improve the efficiency. Finally, we conduct extensive experiments on 12 real-world graphs to evaluate our algorithms. The results show that, when h≥3, our exact and sampling-based algorithms can achieve up to 10x and 100x speedup over the state-of-the-art algorithm, respectively.

Reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems. The extra connectivity and the extra edge-connectivity are two important parameters for the reliability evaluation of interconnection networks. The${\mbi {n}}$-dimensional bijective connection network (in brief, BC network) includes several well known network models, such as, hypercubes, Möbius cubes, crossed cubes, and twisted cubes. In this paper, we explore the extra connectivity and the extra edge-connectivity of BC networks, and discuss the structure of BC networks with many faults. We obtain a sharp lower bound of${{g}}$-extra edge-connectivity of an${\mbi {n}}$-dimensional BC network for${{n}} \geq 4$and$1 \leq { {g}} \leq {2^{[{{{n}} \over 2}]}}$. We also obtain a sharp lower bound of${ {g}}$-extra connectivity of an${{n}}$-dimensional BC network for${{n}} \geq 4$and$1 \leq { {g}} \leq 2{ {n}}$which improves the result in [“Reliability evaluation of BC networks,” IEEE Trans. Computers, DOI: 10.1109/tc.2012.106.] for$1 \leq { {g}} \leq { {n}} - 3$. Furthermore, we give a remark about exploring the${ {g}}$-extra edge-connectivity of BC networks for the more general${\mbi {g}}$, and we also characterize the structure of BC networks with many faulty nodes or links. As an application, we obtain several results on the${\mbi {g}}$-extra (edge-) connectivity and the structure of faulty networks on hypercubes, Möbius cubes, crossed cubes, and twisted cubes.